ATMW Topology (2013)

Venue: IMS, Chennai
Dates: 4th- 9th February , 2013


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name Parameswaran Sankaran 
Mailing Address Institute of Mathematical Sciences,
CIT Campus, Taramani,
Chennai 600113.


Speakers and Syllabus 

Schedule of Lectures: (04th to 09th Feb 2013)

Date/Time 09:30-11:00 11:30-13:00 14:00-15:00 15:30-17:00
Mon C1 C2 P1 D
Tue C1 C3 P2 D
Wed C1 C2 P3 D
Thu C3 C2 P4 D
Fri C1 C3 P5 D
Sat C3 C2 P6 D
Note: C1, C2, C3 stands for the three courses, Pj for participant lectures, and D denotes discussion/tutorial hour.


List of resource persons:

  1. Samik Basu, Vivekananda University, Belur
  2. Goutam Mukherjee, ISI, Kolkata
  3. A. R. Shastri, IIT Bombay, Mumbai

List of courses:

The following three courses are being planned:

  • On homotopy groups of spheres.
  • On Steenrod algebra and its dual (and applications, if there is time).
  • On the complex cobordism ring and the formal group law (with applications, if there is time).

Details of courses:

Homotopy groups of spheres:
Leray-Serre spectral sequence, Serre class of abelian groups, finiteness of homotopy groups πm (Sn ) when m <> n if n is odd (m <> n, 2n − 1 if n is even), Freudenthal suspension theorem, stable homotopy groups of spheres. Postnikov factorization (if time permits).

Steenrod algebra and its dual:
Axioms for the Steenrod operation, The Eilenberg-MacLane spaces, mod-2 cohomology algebra of K(Z/2Z, n). The Steenrod algebra, the dual of the Steenrod algebra, the Hopf algebra structure.

Complex cobordism and formal group law:
Unoriented and oriented cobordism, Complex cobordism, Characteristic numbers, Chern numbers. Bordism theory as via spectra. The structure of the complex cobordism ring. Formal group law–examples. The Lazard ring. Quillen’s theorem. (If there is time, BP cohomology will be discussed.)



Selected Applicants

SID Full Name Gender Affiliation Position in College/Univ. Univ./Institute M.Sc./M.A. Year of Passing M.Sc./M.A Ph.D. Degree Date
2735 Ms. Anusha Mangala Krishnan Female IIT Kanpur Student (Integrated M.Sc.) IIT Kanpur Appeared/ Awaiting Result --
-- Arghya Mondal Male IMSc Chennai SRF IMSc 2012 --
2699 Mr. Arvind Kumar Male HRI, Allahabad PhD BHU, Varanasi 2012 --
2252 Dr Avijit Sarkar Male Univ. of Kalyani, Kalyani Assistant Professor University of kalyani 2002 2 Feb 2010
2713 Mr. Bedanta Bose Male Univ. Of Calcutta, Kolkata Ph.D. Bengal Engineering And Science University, Shibpur 2009 --
2551 Mr. Biplab Basak Male IISc. Bangalore Ph.D. Student IIT Kanpur 2010 --
2574 Dr. J. John Arul Singh Male Noorul Islam Center for Higher Education, Nagercoil Assistant Professor Nesamony Christian College affliated to Manonmaniam Sundaranar University 2007 6 Feb 2012
2778 Mr. Prateep Chakraborty Male IMSc, Chennai PhD University of Calcutta 2008 --
2801 Dr. Priyavrat Deshpande Male CMI, Chennai Post doctoral fellow The university of Western Ontario 2007 30 May 2011
2767 Mr. R Venkatesh          Male IMSc, Chennai SRF Bharathidasan University, Trichy 2009 --
2783 Mr Ramesh Kasilingam Male IIT Bombay PhD Student Anna university, Chennai 2006 --
2768 Dr Ritwik Mukherjee Male IMSc, Chennai Post Doc IIT Kharagpur 2005 20 Dec 2011
2591 Mr Sainkupar Marwein Mawiong Male NEHU, Shillong Asst. Prof. NEHU, Shillong 2004 --
2641 Mr Samir Shukla Male IIT Kanpur PhD Student IIT Delhi 2011 --
2802 Mr Samir Kumar Hazra Male CMI, Chennai PhD IIT Bombay 2011 --
2791 Mr. Satyajit Guin Male IMSc, Chennai PhD IIT Kanpur 2009 --
2529 Dr. Sejal Kiritbhai Shah Female The M. S. Univ. of Baroda. Assistant Professor The M. S. University of Baroda 1997 25 Jan 2007
2752 Dr. Shilpa Suresh Gondhali Female ISI, Kolkata Visiting Scientist University of Mumbai 2005 10 Jul 2012
2333 Ms. Shuchita Goyal Female IIT Bombay PhD IIT Guwahati 2011 --
2763 Dr. Swagata Sarkar Female ISI, Kolkata NBHM Post  doctoral Fellow St. Stephen's College, Delhi University 2003 29 Jan 2010
2273 Mrs. Visalakshi V Female Sri Sarada College for Women, Selem Phd Sri Saradha College for Women 2008 --
2261 Mrs. Yogalakshmi Thangaraj Female Sri Sarada College for Women, Selem Phd University of Madras 2008 --